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Stock-Based Compensation Plans - Narrative (Details) - USD ($) $ / shares in Units, $ in Thousands		12 Months Ended
	Oct. 12, 2021	Aug. 27, 2022	Aug. 28, 2021	Aug. 29, 2020	Aug. 31, 2019	Dec. 11, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Accrued compensation			$ 67,541	$ 36,533
Unrecognized compensation expense related to stock options			$ 1,226
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Outstanding options term			10 years
Vesting period			3 years
Unrecognized compensation expense, period of recognition			9 months 18 days
Performance-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period			3 years
Unrecognized compensation expense			$ 3,804
Unrecognized compensation expense, period of recognition			1 year
Total fair value of awards vested			$ 1,445	$ 2,438
Granted (in shares)			97,996
Vested (in shares)			26,515	0	0
Time-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense			$ 7,122
Unrecognized compensation expense, period of recognition			9 months 18 days
Total fair value of awards vested			$ 5,210	$ 3,324	$ 6,648
Granted (in shares)			150,275
Vested (in shares)			92,942
Time-based | Director
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period			1 year
ESPP
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Discount market price percentage			15.00%
Term of sale restriction period after grant			1 year
Shares purchased through the ESPP (in shares)			24,000	21,000
Accrued compensation			$ 385	$ 274
Restricted Stock Units (RSUs) | Key Management | Subsequent Event
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Granted (in shares)	124,978
Shares granted, value	$ 9,447
Closing price of common stock on grant date (in dollars per share)	$ 75.59
Restricted Stock Units (RSUs) | Key Management | Scenario, Forecast | Subsequent Event
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense		$ 3,149
Incentive Compensation Plan 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)						4,100,000

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Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

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